 | Adrien Marie Legendre - 1822 - 394 σελίδες
...base multiplied by the altitude cannot measure the surface of a greater cylinder. Hence, finally, the convex surface of a cylinder is equal to the circumference of its base, multiplied by the altitude. PROPOSITION V. THEOREM. The solidity of a cone is equal to the product of its base by... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...cylinder is less than that of any Fig. 253. circumscribed prism BCDKLH (fig. 253). THEOREM. 523. The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig. 258. Demonstration. Let CA. (fig. 258) be the radius of the base of the given cylinder, H its... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 σελίδες
...of the cylinder is less than that of any Fig. 253. circumscribed prism BCDKLH (fig. 253). / 523. The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude. Fig. 258. Demonstration. Let CA (fig. 258) be the radius of the base of the given cylinder, H its altitude... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...cylinder is less than that of any Pig. 253. circumscribed prism BCDKLH (fig. 253). THEOREM. 523. The convex surface of a cylinder is equal to the circumference of its base midliplied by its altitude. Fig. 258. Demonstration. Let CA (Jig. 258) be the radius of the base of... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...Again, lemma 522 may be omitted, being only introduced for the sake of demonstrating theorem 523. The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude. Now it has already been demonstrated, lemma 520, that ' the convex surface of a right prism, is equal... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...Again, lemma 522 may be omitted, being only introduced for the sake of demonstrating theorem 523. The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude. Now it has already been demonstrated, lemma 520, that ' the convex surface of a right prism, is equal... | |
 | Adrien Marie Legendre - 1828 - 346 σελίδες
...fig. of Art. 512.) THEOREM. 523. The convex surface of a cylinder is equal to the circumference of Us base multiplied by its altitude. Let CA be the radius of the given cylinder's base, H its altitude ; the circumference whose radius is CA, being represented by circ. CA, we are to show... | |
 | Timothy Walker - 1829 - 138 σελίδες
...that the convex surface=C x A, for (C x R) + (C x A) = ( A+R) x C. We are to demonstrate that — the convex surface of a cylinder is equal to the circumference- of its base multiplied by its altitude — . This will be evident if it be admitted that — the cylinder is a right prism of an infinite... | |
 | Adrien Marie Legendre - 1830 - 344 σελίδες
...be less than that of any circumscribed prism BCDKLH. (See the fig. of Art. 512.) THEOREM. 533. The con-vex surface of a cylinder is equal to the circumference...Let CA be the radius of the given cylinder's base, H its altitude ; the circumference whose radius is CA, being represented by arc. CA, we are to show... | |
 | Charles Davies - 1840 - 262 σελίδες
...cylinder. This cylinder is said to circumscribe the sphere. 27. It was remarked, in Art. 4, that the convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude ; and in Art. 24, that the surface of a sphere is equal to its diameter into the circumference of a... | |
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The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig. 
